You walk 12 km south and then 5 km east.Your resultant displacement is
A)13 km at an angle of 22.6º south of east.
B)13 km at an angle of 67.4º south of east.
C)17 km at an angle of 22.6º south of east.
D)17 km at an angle of 67.4º south of east.
E)None of these is correct.

Question

Quizplus · Accepted Answer

The resultant displacement can be found by drawing a right-angled triangle with one side of length 12 km and the other side of length 5 km. The hypotenuse of this triangle represents the resultant displacement.

Using the Pythagorean theorem, we find that the length of the hypotenuse is:

√(12² + 5²) = √(144 + 25) = √169 = 13 km

To find the angle that the resultant displacement makes with the south direction, we use the tangent function:

tanθ = opposite/adjacent = 5/12
θ = tan⁻¹(5/12) = 22.6º

However, we want to find the angle that the resultant displacement makes with the east direction, which is 90º - θ:

90º - 22.6º = 67.4º

So the resultant displacement is 13 km at an angle of 67.4º south of east, which is choice B.

You Walk 12 Km South and Then 5 Km East